Level set methods for gradient-free optimization of metasurface arrays

TL;DR

This paper introduces a level set method with a novel periodic parameterization for gradient-free optimization of metasurface arrays, improving design efficiency and electromagnetic performance, validated through real-world measurements.

Contribution

It presents a new periodic level set parameterization and a pseudo-inverse upsampling technique, enhancing the optimization process for metasurfaces compared to existing methods.

Findings

Improved electromagnetic responses with the new level set method.

Demonstrated real-world metasurface performance through manufacturing and measurements.

Enhanced optimization convergence for broadband and narrowband objectives.

Abstract

Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in ensuring computational efficiency and convergence of the optimization algorithm to a globally optimal solution. While many design variables in physical systems take discrete values, optimization algorithms often benefit from a continuous design space. This work demonstrates the use of level set functions as a continuous basis for designing material distributions for metasurface arrays and introduces an improved parameterization which is termed the periodic level set function. We explore the use of alternate norms in the definition of the level set function and define a new pseudo-inverse technique for upsampling basis coefficients with these norms. The level set method is compared to the fragmented parameterization and shows improved electromagnetic responses for two dissimilar cost functions: a narrowband objective and a broadband objective. Finally, we manufacture an optimized level set metasurface and measure its scattering parameters to demonstrate real-world performance.